Our description of time reversal has been quite schematic, so let us now be more precise. In fact the technical details of how to implement an appropriate reversal operation are non-trivial, because this requires making a clean separation between the time-symmetric underlying physics and the asymmetries introduced by assumptions about the role of agents, and these features can be difficult to distinguish. Currently, it is known that at least some causal processes are time-reversal invariant in a sense made precise by Pienaar[1]}. Given an IS description of a quantum process, Pienaar shows how to write down the corresponding OS process using symmetric informationally complete (SIC) quantum instruments, and then proves that if the directed acyclic graph G associated with the process in the IS description has a certain structure (a `layered' structure) and the process matrix W associated with the IS description is unbiased (inputting the maximally-mixed-state to the process produces the maximally-mixed state as output), then the process is causally reversible, i.e. the OS process is compatible with another IS descrption whose graph is obtained by reversing the direction of all the arrows in G. That is to say, for at least some causal processes it is indeed the case that we can reverse the IS description to obtain an alternative IS description which corresponds to the same underlying OS process, and moreover this reversed description will still be causal. It's unclear whether some result of this kind could be extended to all causal processes, but we do know that all physically possible processes can be obtained from `pure' processes by tracing out an ancilla system[2]}, and `pure' processes are those which induce a unitary (and hence reversible) transformation from the past to the future whenever unitary transformations are also applied in the local laboratories; so it appears that causal processes can indeed be derived from time-reversal invariant underlying physics, and therefore it would seem reasonable to conjecture that all causal processes should be reversible according to an appropriate formulation of operational time reversal, or at least can be extended using an ancilla to a process which is reversible in this way.
